Sure, let's break this down step-by-step.
First, we need to convert the mixed fraction [tex]\( 3 \frac{1}{6} \)[/tex] into an improper fraction.
Step 1: Convert the mixed number to an improper fraction.
[tex]\[ 3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{18 + 1}{6} = \frac{19}{6} \][/tex]
Step 2: We express the given fraction in the form [tex]\( \sqrt[3]{a} \)[/tex].
Now, we need to solve for [tex]\( a \)[/tex]:
[tex]\[ \left( \frac{19}{6} \right)^3 = a \][/tex]
Step 3: Calculate the value of [tex]\( a \)[/tex]:
[tex]\[ a = 31.754629629629626 \][/tex]
So, the expression [tex]\( 3 \frac{1}{6} \)[/tex] written in the form [tex]\( \sqrt[3]{a} \)[/tex], results in [tex]\( a = 31.754629629629626 \)[/tex].
Therefore, [tex]\( a = 31.754629629629626 \)[/tex] and there is no value for [tex]\( b \)[/tex]; hence we can leave the second box empty.
Thus, the final answers are:
[tex]\[ a = 31.754629629629626 \][/tex]
[tex]\[ b = \emptyset \][/tex]
